1. Technical Field
This invention relates generally to a method and apparatus f or filtering an image, and more specifically, to a method and apparatus for filtering and thereby removing background clutter from an image of an imaging and targeting system.
2. Discussion of the Related Art
Image processing systems which autonomously acquire or track a target moving against a cluttered background are known in the art. To accurately track the target, these systems must employ background clutter suppression methods to reduce or eliminate the background clutter, and thus, more dependably track the target. In a long range target acquisition situation targets tend to be unresolved, and therefore are difficult to detect. Background suppression requirements for these types of systems are generally severe, because the tracking system must have a low probability of both missed target detection and false target detection. A high signal to noise ratio is also important. Some prior art methods have attempted to suppress background clutter by means of filters.
One prior art method of filtering background clutter in an autonomous image tracking system, well known to those skilled in the art, is the use of linear spatial filters. A linear filter produces an output which is a linear combination of the elements in a particular processing "window".
A second background clutter filtration method makes use of median and anti-median filters. Median and anti-median filters are non-linear operators in which the individual elements within a processing "window" are ordered and ranked on the basis of amplitude. The output of such a filter is then determined as a specific rank from the collection of amplitudes. These filters eliminate the background clutter on the basis of feature size. A more detailed description of the principles of median and anti-median filters is given below.
A "median" is defined as that value of a group of values which exceeds the values of as many members of the group as it is exceeded by. For example, consider the group of integers (7, 3, 9, 8, 6, 4, 6). Since this set of values has seven numbers, the median of the group will be the fourth largest (or fourth smallest) value. For this sample, 6 is the median since there are three numbers which exceed it and three numbers which it equals or exceeds. In other words, a median value of a set of values is determined by arranging the values in order of ascending (or descending) magnitude, and then selecting the value in the middle of the list. As such, a median can only be defined in terms of a set which has an odd number of values or elements. A median filter is an operator which outputs the median value of an odd numbered group of elements.
An "anti-median" filter is a non-linear operator in which the output of the median filter is subtracted from the value at the geometric center of the original sample group of elements. For example, the center value of the group of elements (7, 3, 9, 8, 6, 4, 6) has a value of 8. Therefore, to calculate the anti-median value we would subtract six from eight (8-6). The output of the anti-median filter would thus be two (2). If the median value occupies the geometric center of the sample, such as in the sample group (7, 3, 9, 6, 8, 4, 6), the anti-median value would have been (6-6)=0.
If an anti-median filter processes a random sequence of values from a common statistical sample, the median value will be at the geometric center of the sample with a probability of at least (1/N), where N is the number of elements in the sample. If the sample size is N=5, then the output of the anti-median filter would be zero 20% of the time.
A probability density function of the output of the anti-median filter can be calculated which would include a certain value at the origin representative of the probability that the anti-median filter output would equal zero (0). Since the cumulative probability obtained by integrating the probability density function from -.infin. to +.infin. must equal one, the value at the origin of the probability density function will reduce the total remaining area. This property is responsible for the useful noise reduction and clutter suppression properties of the anti-median filter.
It can be shown that a median filter which scans a sample set of an image will suppress or attenuate relatively small objects, whereas an anti-median filter scanning a sample set of an image will attenuate or suppress relatively large objects. Consider the following string of sample values: 0, 0, 0, 0, 3, 3, 3, 0, 0, 0, 0, 1, 0, - - - . It may help to visualize each integer as representative of the magnitude of the intensity of specific pixel elements of an image. Here, the value 0 is a pixel value whose intensity does not exceed a predetermined threshold limit. The value 3 represents higher intensity pixels, and the subset 3,3,3 would be a "blob" in the image. The value 1 is an intensity value which just exceeds the threshold limit and may be the target of interest.
Now consider a scanning median filter which takes the sample set above in five element arrays. The first scanned set would be (0,0,0,0,3). From the discussion above, the output of the median filter would be zero (0) since there would be two (2) values in the set less than or equal to zero (0), and two (2) values in the set greater than or equal to zero (0). For the next set of five elements from the scanning process, i.e., (0,0,0,3,3) the result would be the same. For the next set, i.e., (0,0,3,3,3,) the output would be three (3). This scanning sequence can be continued to get the sequence values of 0,0,3,3,3,0,0,0,0,0,0 - - - as the output of the median filter. It is noted that the sample value 1 has been eliminated. Also from the discussion above for an anti-median value, it can be shown that this sequence of sample elements for an output of an anti-median filter would be 0,0,0,0,0,0,0,0,0,0,1,0, - - - . Here the relatively large values of 3 have been eliminated. Consequently, the "blob" (3,3,3) has been eliminated, and the target of interest (1) has been isolated.
From this analysis it can be shown that a median filter suppresses any object whose size is less than (N+1)/2 pixels or sample values, where N is the number of elements in the sample array. For the above example, N=5, and thus the median filter would suppress any "blob" smaller in size than 3 sample values. An anti-median filter, on the other hand, performs in a complementary manner by preserving all objects whose sizes are less than (N+1)/2. Conceptually, this can be understood in practice by visualizing a distant target against a background scene. The target will appear as a much smaller image signal against the background signals. Consequently, the anti-median filter can be calibrated to suppress any image (signal) larger than a predetermined size; thus, background signals larger than the target signal can be substantially eliminated.
Although an anti-median filter reduces or attenuates large objects, there are many cases where background residues (background leakage) remains unacceptably large. One particularly troublesome type of background leakage is caused by line-like objects in the background clutter. This problem is especially severe if these line segments are oriented perpendicular to the direction of scanning.
Regardless of this drawback, anti-median filters have unique properties which make them superior to linear filters for background suppression applications. For example, they do not produce pre-shoots, overshoots or ringing phenomena when their inputs comprise impulse or step-like functions. Further, they do not attenuate signal components as a function of frequency.
What is needed then is a background clutter suppression filter which includes the unique properties of an anti-median filter, but which substantially reduces many of the background leakage problems generally associated with these types of filters. It is therefore an object of the present invention to provide such a filter.